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Frequency-Resolved Optical Gating Recovery via Smoothing Gradient

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2019年第23期67卷 6121-6132页

作者： Pinilla, Samuel Bendory, Tamir Eldar, Yonina C. Arguello, Henry Univ Indtrial Santander Dept Elect Engn Bucaramanga 680002 Colombia Princeton Univ Program Appl & Computat Math Princeton NJ 08544 USA Weizmann Inst Sci IL-7610001 Rehovot Israel Univ Ind Santander Dept Comp Sci Bucaramanga 680002 Colombia

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://***/samuelpinilla/FROG.

关键词： Signal processing algorithms Approximation algorithms Fourier transforms Optical pulses Smoothing methods Optical imaging Optical pulse generation Pulse reconstruction spectral algorithm FROG ultrashort pulse characterization phase retrieval smoothing gradient technique

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Satellite Estimation of Chlorophyll-a Concentration Using the Red and NIR Bands of MERIS-The Azov Sea Case Study

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2009年第4期6卷 845-849页

作者： Moses, Wesley J. Gitelson, Anatoly A. Berdnikov, Sergey Povazhnyy, Vasiliy Univ Nebraska Sch Nat Resources Ctr Adv Land Management Informat Technol Lincoln NE 68583 USA Russian Acad Sci So Sci Ctr Rostov Na Donu 344000 Russia

We present here the results of calibrating and validating a three-band model and, its special case, a two-band model, which use MEdium Resolution Imaging Spectrometer (MERIS) reflectances in the red and near-infrared spectral regions for estimating chlorophyll-a (chl-a) concentration in inland, estuarine, and coastal turbid productive waters. During four data collection campaigns in 2008 and one campaign in 2009 in the Taganrog Bay and the Azov Sea, Russia, water samples were collected, and concentrations of chl-a and total suspended solids were measured in the laboratory. The data collected in 2008 were used for model calibration, and the data collected in 2009 were used for model validation. The models were applied to MERIS images acquired within two days from the date of in situ data collection. Two different atmospheric correction procedures were considered for processing the MERIS images. The results illustrate the high potential of the models to estimate chl-a concentration in turbid productive (Case II) waters in real time from satellite data, which will be of immense value to scientists, natural resource managers, and decision makers involved in managing the inland and coastal aquatic ecosystems.

关键词： Chlorophyll-a (chl-a) MEdium Resolution Imaging Spectrometer (MERIS) remote sensing spectral algorithm turbid productive waters

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Clusters detection based leading eigenvector in signed networks

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 523卷 1263-1275页

作者： Ma, Yinghong Zhu, Xiaoyu Yu, Qinglin Shandong Normal Univ Business Sch Jinan Shandong Peoples R China Thompson Rivers Univ Dept Math & Stat Kamloops BC Canada Xian Polytech Univ Sch Sci Xian Shaanxi Peoples R China

The structural balance theory offers a comprehensive way to understand stability and tensions in social systems. However, most of the real social networks are unbalanced in which people are not exclusively divided into groups such that people within a group are friendly to each other but hostile to everyone in other groups. That is, there are conflict edges in a partition regardless of how we divide people in a given social network. The natural question to ask is that how many conflict edges should be changed to make a network balanced. Alternatively, the clustering problem is formulated to optimize minimum conflicts or maximum balanceness. In this paper, utilizing the relationship between balancedness and spectrum space, we propose a spectral algorithm based leading eigenvectors of signed networks to partition clusters and make balancedness maximum. The spectral algorithm is a two stages approach, partition subnetworks corresponding to temporary clusters to increase the objective value and fine-tune partition based on the fitness of nodes. The robustness of the algorithm is completely dependent on the adjacent matrixes of signed networks. And it can measure the balanceness of network in global way with the lowest errors. The experimental results on both real signed networks and synthetic networks demonstrate that the leading eigenvector based method is highly effective and accuracy. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Signed network spectral algorithm Leading eigenvector Clusters Conflicts

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A Statistical Model for Motifs Detection

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第12期64卷 7594-7612页

作者： Javadi, Hamid Montanari, Andrea Stanford Univ Dept Elect Engn Stanford CA 94305 USA

We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks, small subgraphs with a specific structure have important functional roles, and they are referred to as motifs. Within this model, one or multiple copies of a subgraph is added (planted) in an Erdos-Renyi random graph with n vertices and edge probability q(0). We ask whether the resulting graph can be distinguished reliably from a pure Erdos-Renyi random graph, and we present two types of result. First we investigate the question from a purely statistical perspective, and ask whether there is any test that can distinguish between the two graph models. We provide necessary and sufficient conditions that are essentially tight for small enough subgraphs. Next we study two polynomial-time algorithms for solving the same problem: a spectral algorithm and a semidefinite programming (SDP) relaxation. For the spectral algorithm, we establish sufficient conditions under which it distinguishes the two graph models with high probability. Under the same conditions the spectral algorithm indeed identifies the hidden subgraph. The spectral algorithm is substantially sub-optimal with respect to the optimal test. We show that a similar gap is present for the more sophisticated SDP approach.

关键词： Motifs Erdos-Renyi random graph hypothesis testing spectral algorithm semidefinite relaxation

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Normalized difference chlorophyll index: A novel model for remote estimation of chlorophyll-a concentration in turbid productive waters

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REMOTE SENSING OF ENVIRONMENT 2012年 117卷 394-406页

作者： Mishra, Sachidananda Mishra, Deepak R. Mississippi State Univ Dept Geosci Mississippi State MS 39762 USA Mississippi State Univ Geosyst Res Inst Mississippi State MS 39762 USA Mississippi State Univ No Gulf Inst Mississippi State MS 39762 USA

We propose a normalized difference chlorophyll index (NDCI) to predict chlorophyll-a (chl-a) concentration from remote sensing data in estuarine and coastal turbid productive (case 2) waters. NDCI calibration and validation results derived from simulated and MEdium Resolution Imaging Spectrometer (MERIS) datasets show its potential application to widely varying water types and geographic regions. A quadratic function (R-2=0.95, p<0.0001) accurately explained the variance in the simulated data for a chl-a range of 1-60 mg m(-3). Similarly a twofold calibration and validation of chl-a models using MERIS dataset, (chl-a range: 0.9-28.1 mg m(-3)) yielded R-2 of 0.9, and RMSE of similar to 2 mg m(-3) respectively. NDCI was applied on images over the Chesapeake Bay and Delaware Bay, the Mobile Bay, and the Mississippi River delta region in the northern Gulf of Mexico. The newly developed algorithm was successful in predicting chl-a concentration with approximately 12% overall bias for all above study regions. Findings from this research imply that NDCI can be successfully used on MERIS images to quantitatively monitor chl-a in inland coastal and estuarine waters. In case of remote coastal waters with no ground truth data. NDCI can be used to detect algal bloom and qualitatively infer chl-a concentration ranges very similar to NDVI's application in terrestrial vegetation studies. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Chlorophyll-a Normalized difference chlorophyll index Remote sensing reflectance spectral algorithm Turbid productive waters MEdium Resolution Imaging Spectrometer

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Multireference Alignment Is Easier With an Aperiodic Translation Distribution

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第6期65卷 3565-3584页

作者： Abbe, Emmanuel Bendory, Tamir Leeb, William Pereira, Joao M. Sharon, Nir Singer, Amit Princeton Univ Program Appl & Computat Math Princeton NJ 08544 USA Princeton Univ Dept Elect Engn Princeton NJ 08544 USA Univ Minnesota Twin Cities Sch Math Minneapolis MN 55455 USA Tel Aviv Univ Sch Math Sci IL-6997801 Tel Aviv Israel Princeton Univ Dept Math Princeton NJ 08544 USA

In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (SNR) (the signal energy divided by the noise variance) in order to drive the mean-square error to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as omega(1/SNR3). In this paper, using a generalization of the Chapman-Robbins bound for orbits and expansions of the chi(2) divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as omega(1/SNR2). This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation-maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model.

关键词： Multireference alignment spectral algorithm method of moments spiked covariance model non-convex optimization expectation-maximization cryo-EM

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Community structure in traffic zones based on travel demand

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2016年 457卷 356-363页

作者： Sun, Li Ling, Ximan He, Kun Tan, Qian Cent South Univ Sch Traff & Transportat Engn Changsha 410000 Hunan Peoples R China

Large structure in complex networks can be studied by dividing it into communities or modules. Urban traffic system is one of the most critical infrastructures. It can be abstracted into a complex network composed of tightly connected groups. Here, we analyze community structure in urban traffic zones based on the community detection method in network science. spectral algorithm using the eigenvectors of matrices is employed. Our empirical results indicate that the traffic communities are variant with the travel demand distribution, since in the morning the majority of the passengers are traveling from home to work and in the evening they are traveling a contrary direction. Meanwhile, the origin-destination pairs with large number of trips play a significant role in urban traffic network's community division. The layout of traffic community in a city also depends on the residents' trajectories. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Urban traffic system Traffic community division Community detection spectral algorithm

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AN IMPOSSIBILITY RESULT FOR RECONSTRUCTION IN THE DEGREE-CORRECTED STOCHASTIC BLOCK MODEL

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ANNALS OF APPLIED PROBABILITY 2018年第5期28卷 3002-3027页

作者： Gulikers, Lennart Lelarge, Marc Massoulie, Laurent Microsoft Res INRIA Joint Ctr Campus Ecole PolytechBatiment Alan Turing F-91120 Palaiseau France INRIA Paris 2 Rue Simone IffCS 42112 F-75589 Paris 12 France Ecole Normale Super Paris France

We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on n nodes, having i.i.d. weights (phi u)(u)(n)=i (possibly heavytailed), partitioned into q >= 2 asymptotically equal-sized clusters. The model parameters are two constants a, b > 0 and the finite second moment of the weights Phi((2)). Vertices u and v are connected by an edge with probability phi u phi v/na when they are in the same class and with probability phi u phi v/nb otherwise. We prove that it is information-theoretically impossible to estimate the clusters in a way positively correlated with the true community structure when (a - b)(2) (Phi)((2)) <= q (a + b). As by-products of our proof we obtain (1) a precise coupling result for local neighbourhoods in DC-SBMs, that we use in Gulikers, Lelarge and Massoulie (2016) to establish a law of large numbers for local-functionals and (2) that long-range interactions are weak in (power-law) DC-SBMs.

关键词： Social and information networks random graphs degree-corrected stochastic block model spectral algorithm machine learning

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Synthesis of a robust optimal system for stabilizing a plant with failing elements

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CYBERNETICS AND SYSTEMS ANALYSIS 2000年第3期36卷 442-449页

作者： Blokhin, LN Kazak, VN Int Univ Civil Aviat Kiev Ukraine

An original performance functional is proposed for problems of synthesis of highly accurate stabilizing systems, which consist of an element that is a measure of the sensitivity of the closed-loop system to arbitrary changes of the controlled plant. A new spectral algorithm is considered for the synthesis of optimal stabilizing systems. An analytical example of the synthesized system is given to illustrate the high efficiency of the synthesis procedure.

关键词： stabilizing system performance functional spectral algorithm

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LEARNING SPARSE GRAPHONS AND THE GENERALIZED KESTEN-STIGUM THRESHOLD

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ANNALS OF STATISTICS 2023年第2期51卷 599-623页

作者： Abbe, Emmanuel Li, Shuangping Sly, Allan Ecole Polytech Fed Lausanne Inst Math Lausanne Switzerland Princeton Univ PACM Princeton NJ USA Princeton Univ Dept Math Princeton NJ USA

The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the re-cent years in sparser regimes. Yet, the current techniques still require diverg-ing degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper pro-vides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succeed in estimating the rank-k projec-tion of a graphon in the L2 metric if the top k eigenvalues of the graphon satisfy a generalized Kesten-Stigum condition.

关键词： Inference on networks graphon spectral algorithm

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